B1 mapping by Bloch-Siegert shift

Abstract

A novel method for amplitude of radiofrequency field (B1+) mapping based on the Bloch-Siegert shift is presented. Unlike conventionally applied double-angle or other signal magnitude-based methods, it encodes the B(1) information into signal phase, resulting in important advantages in terms of acquisition speed, accuracy, and robustness. The Bloch-Siegert frequency shift is caused by irradiating with an off-resonance radiofrequency pulse following conventional spin excitation. When applying the off-resonance radiofrequency in the kilohertz range, spin nutation can be neglected and the primarily observed effect is a spin precession frequency shift. This shift is proportional to the square of the magnitude of B1(2). Adding gradient image encoding following the off-resonance pulse allows one to acquire spatially resolved B(1) maps. The frequency shift from the Bloch-Siegert effect gives a phase shift in the image that is proportional to B(1)(2). The phase difference of two acquisitions, with the radiofrequency pulse applied at two frequencies symmetrically around the water resonance, is used to eliminate undesired off-resonance effects due to amplitude of static field inhomogeneity and chemical shift. In vivo Bloch-Siegert B(1) mapping with 25 sec/slice is demonstrated to be quantitatively comparable to a 21-min double-angle map. As such, this method enables robust, high-resolution B(1)(+) mapping in a clinically acceptable time frame.

Figure 1

B₁ field in the rotating frame of the RF. The frame rotates at frequency ω₀ + ω_RF. In this frame, the B₁ field is static, where as the spins rotate at ω_RF. The Bloch-Siegert frequency shift ω_BS is a constant field in this rotating frame along the effective RF field vector γB₁^eff.

Figure 2

Percentage error in B₁ calculation as a function of B₀ offset over a range of 1 kHz. The error is calculated from Eqns. 11 and 12, for RF pulses at off-resonance frequencies of 2, 4, 8 kHz.

Figure 3

Gradient and spin echo sequences, modified for B₁ mapping. The gradient echo sequence has an 8 msec off-resonance Fermi pulse at off-resonance frequency ω_RF following excitation. The spin echo sequence has two 6 msec off-resonance Fermi pulses. The first pulse is at off-resonance frequency ω_RF and the second at −ω_RF .

Figure 4

Normalized B₁(t) and corresponding frequency excitation profile for an 8 msec Fermi pulse, and ω_RF = 4 kHz.

Figure 5

Phase shift φ_BS vs. |B₁| for an 8 msec Fermi pulse at 4 kHz. Simulated by the analytical expression of Eqn. 6, and numerical Bloch simulation.

Figure 6

Comparison of four RF pulses, all of 8 msec pulse length, at 4 kHz off-resonance, relative to water. The hard pulse, Fermi, adiabatic hyperbolic secant (with a time varying frequency sweep ω_RF(t) of +/−2kHz around 4 kHz), and the adiabatic tanh/tan pulse (with a time varying frequency sweep ω_RF(t) of +/−20kHz around 4 kHz). K_BS (radians/gauss²) is calculated for these four pulses, as well as the frequency range that contains 99% of spin excitation. This Fermi pulse is used for all subsequent experiments shown here.

Figure 7

a. Double angle B₁ map, calculated from two scans acquired with a 3.2 msec sinc pulse having flip angles of α = 60°, 2α = 120°, TE = 10 msec, TR = 5 sec. Slice thickness = 1 cm, 128×128 resolution. b. Gradient echo Bloch-Siegert B₁ map, acquired with TE = 15 msec, TR = 70 msec (left), 2 sec. (right), 8 msec, +/−4 kHz Fermi pulse. c. Error between the two methods: Double Angle map / Bloch-Siegert map * 100% d. B₁ maps acquired with the amplifier output at 0.33, 0.5, 0.75, 1.0, 1.5 * B_1,peak, where B_1,peak = 0.073 gauss B₁ field produced at the center of the slice. The B₁ maps are displayed rescaled to 0.073 gauss for comparison. e. Bloch-Siegert B₁ maps of a saline phantom with three milk compartments acquired with the 8 msec Fermi pulse at off-resonance frequencies of 2, 4, 6, and 8 kHz relative to the water resonance.

Figure 8

a, b. Magnitude gradient echo images with 8 msec off-resonance Fermi pulse, ω_RF = +/− 4 kHz. c. Same image acquisition, without the off-resonance pulse. d. Double angle B₁ map, 128×128, slice thickness = 0.5 mm, TE = 12 msec, TR = 3 sec. Flip angles α = 45° 2α = 90°. e. Bloch Siegert map calculated from the phase difference between images a. and b. The peak B₁ of the Bloch-Siegert map was twice the peak B₁ used in the double angle map. Resolution 128×128, slice thickness = 0.5 mm, TE = 12 msec, TR = 100 msec, off resonance pulse: 8 msec Fermi, ω_RF = +/− 4 kHz.

Figure 9

a. Double angle B₁ map, resolution 128×128, slice thickness = 0.5 mm, TE = 12 msec, TR = 5 sec. Flip angles α = 60° 2α = 120°. b. Gradient echo Bloch-Siegert map, resolution 128×128, slice thickness = 0.5 mm, TE = 12 msec, TR = 100 msec, off resonance pulse: 8 msec Fermi, ω_RF = +/− 4 kHz.

Figure 10

Spin echo Bloch-Siegert B₁ maps, acquired with two 6 msec, +/− 4 kHz off-resonance Fermi pulses, applied symmetrically around a 3.2 msec sinc refocusing pulse. The Fermi pulses had the same peak B₁ as the excitation pulse. TE = 28 msec, TR = 200 msec, resolution = 128×128, slice thickness = 1 cm. a. Shoulder, two subjects, taken with GE DVMR whole body transmit/receive coil. b. Abdomen, axial orientation two subjects, taken with whole body transmit, GE 8-channel torso receive array. c. Abdomen, sagittal and coronal orientations.